Question

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determine the relationship between the two triangles and whether or not they can be proven to be congruent.

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the two triangles are related by ​, so the triangles ​.

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Explanation:

Step1: Analyze Triangle Angles and Orientation

Both triangles are right - angled (have a 90 - degree angle). The first triangle can be rotated (for example, a 90 - degree rotation or a reflection - rotation combination) to match the orientation of the second triangle. Rotation is a type of rigid transformation. Rigid transformations (rotation, reflection, translation) preserve the shape and size of a figure.

Step2: Determine Congruence Based on Rigid Transformations

Since rotation is a rigid transformation, and the triangles have the same shape (both right - angled) and, assuming the side lengths corresponding to the right - angled triangles are equal (from the visual similarity and the fact that rigid transformations preserve size), the two triangles are related by rotation. And because rotation is a rigid transformation that preserves congruence, the triangles are congruent.

Answer:

The two triangles are related by rotation, so the triangles are congruent.